NEET Class neet Answered

Explain concept of current leads or lags voltage by 90

Asked by rathod1234sujal | 15 Nov, 2022, 19:10: PM

Expert Answer

Let us consider an inductor of inductance L is connected across a AC voltage source as shown in figure.

Let the alternating voltage v across the voltage source is

ξ = v_m sin(ω t )......................................(1)

where v_m is peak voltage and ω is angular frequency .

Voltage across inductor is given as L (dI/dt )

Hence we have , L (dI/dt ) = v_m sin(ωt )

dI = ( v_m / L ) sin(ωt )

Current through the inductor is determined by integrating above expression

begin mathsize 14px style I subscript L space equals space minus space open parentheses fraction numerator v subscript m over denominator L space omega end fraction close parentheses space cos left parenthesis omega t right parenthesis space equals space space stretchy left parenthesis fraction numerator v subscript m over denominator L space omega end fraction stretchy right parenthesis space sin open parentheses omega t space minus space pi over 2 close parentheses end style

................................(2)

where Lω is known inductive reactance

If we compare eqn.(1) and (2) , we see that phase of current lags by π/2 or quarter cycle

in comparision to the phase of voltage . This is illustrated in the figure given below

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Let us consider now , a capacitor is connected across the alternating voltage source.

Voltage across capacitor , v = q /C

since current is rate of flow of charge , i = dq/dt = C ( dv/dt )

Using eqn.(1) , we get ,

begin mathsize 14px style i space equals space fraction numerator v subscript m over denominator 1 divided by left parenthesis C omega right parenthesis end fraction space cos left parenthesis omega t right parenthesis space equals space space fraction numerator v subscript m over denominator 1 divided by left parenthesis C omega right parenthesis end fraction space sin space left parenthesis omega t space plus space pi over 2 right parenthesis end style

...........................(3)

where 1/(Cω) is capacitive reactance .

if we compare eqn.(1) and eqn.(3) , we see that phase of current leads by π/2 or one quarter of cycle .

This is illustrated in the figure given below

Answered by Thiyagarajan K | 16 Nov, 2022, 17:45: PM

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